Can I connect a Diffuse BSFD to the Principled BSDF's roughness input?
No you can't connect a shader's output to a the input of another shader. Different kind inputs should not be mixed. Green goes with green, purple with purple, Yellow and Grey can be mixed if you know what you are doing.

Refer to these links to understand what each color socket is for:

What is the meaning of the color of the node sockets in the node editor?

and

Cycles - (Shader) Nodes - inputs outputs - What are the exact data types?

Normal maps and roughness maps are different kind of information and each of them can be connected to their corresponding input.

Normal map would go to the normal input socket.

Roughness to roughness input on the same principled BDSF node.